Dave's Web Corner

MTH-264 Week 14 (April 6-12)

• Outline
• Assessments
• Handouts
• Videos
• Technology

Outline

6.3 Second-Order Equations

• recommended: 7, 11, 15, 16, 18, 23, 26, 27, 28, 29, 30, 30 alt, 31, 32, 34
• basic constant "juggling"
• concentration on the shifting theorems
  • the first shifting theorem
    • If L[ f(t) ] = F(s), then L[ e^atf(t) ] = F(s-a)
    • "wrapping a function in an exponential envelope results in shifting its transform"
  • the second shifting theorem
    • If L[ f(t) ] = F(s), then L[ u_a(t) f(t-a) ] = e^-asF(s)
    • "wrapping a transform in an exponential envelope is the result of a 'shift and delay' of the original function"
• advanced constant "juggling"
• the transform of higher-order derivatives
• manipulating sines and cosines
• discontinuous forcing functions

6.4 Delta Functions and Impulse Forcing

• recommended: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
• the dirac function
• a basic example
• periodic impulse forcing
• the effect on graphs of solutions

Assessments

• Deadlines and File Submission
  • Submit your assessment as a single PDF file to the Assessment Folder inside your assigned Google Drive folder by 11:59pm on the date indicated.
  • No late assessments are accepted. If you have a conflict with a deadline, contact me before the deadline.
  • Solutions are posted under these links after the deadline.
• Homework
  • due Wednesday, April 9: Appendix B - 12 alt, 18 alt, 6.1 - 22 alt, 25 alt, 6.2 - 13 alt, 14 alt
  • due Wednesday, April 16: 6.3 - , 6.4 -
  • due Wednesday, April 23: 6.4 - , 6.5 -
• Exams
  • due Wednesday, April 23: Exam 3
    • Exam 3 (solutions)
    • Exam 3 covers sections 3.6, 4.1-4.4, appendix B, and 6.1-6.5

Handouts

• Announcements
  • Schmidt Award
  • Math Graduate Award
  • Honors Program introduction
  • Tutoring Center services
• Technology Tips
  • Download and Install Mathematica
  • Install DETools
  • TI-89 Slope Fields
  • TI-89 Direction Fields
• Series Solutions
  • Famous Power Series
  • Convergence Tests
• Laplace Transforms
  • Laplace Transform Facts
  • Laplace Transform Practice
  • Laplace Transform Solutions
  • Comparing Four Methods
  • Laplace Transform Trigonometry Derivations

Videos

• Laplace Transformations
  • Laplace Transform Definition
  • The Linearity of the Transform
  • The Transform of a Derivative
  • The Inverse Transform
  • A Basic Solution
  • Juggling Constants
  • Partial Fraction Decomposition
  • Shift and Delay
  • The First Shifting Theorem
  • The Heaviside Function
  • Heaviside Function Transformed
  • The Second Shifting Theorem
  • Shifting Theorems Applied
  • Dirac Function Transformed

Technology

• Communication
  • Zoom
  • Joining a Zoom Webinar
• Excel
  • Euler First-Order Equation.xlsx
  • Euler First-Order System.xlsx
• Mathematica
  • Basic Solution Check.nb
  • Dirac and Heaviside Solutions.nb
  • Discontinuous Driving Functions.nb
  • Periodic Impulse Forcing Example.nb
  • Fast 13 Concept - Defeating Speed Bumps.nb